Mathematical and statistical functions for the Quartic kernel defined by the pdf, $$f(x) = 15/16(1 - x^2)^2$$ over the support \(x \in (-1,1)\).
distr6::Distribution -> distr6::Kernel -> Quartic
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
pdfSquared2Norm()The squared 2-norm of the pdf is defined by $$\int_a^b (f_X(u))^2 du$$ where X is the Distribution, \(f_X\) is its pdf and \(a, b\) are the distribution support limits.
Quartic$pdfSquared2Norm(x = 0, upper = Inf)
x(numeric(1))
Amount to shift the result.
upper(numeric(1))
Upper limit of the integral.
cdfSquared2Norm()The squared 2-norm of the cdf is defined by $$\int_a^b (F_X(u))^2 du$$ where X is the Distribution, \(F_X\) is its pdf and \(a, b\) are the distribution support limits.
Quartic$cdfSquared2Norm(x = 0, upper = 0)
x(numeric(1))
Amount to shift the result.
upper(numeric(1))
Upper limit of the integral.
variance()The variance of a distribution is defined by the formula $$var_X = E[X^2] - E[X]^2$$ where \(E_X\) is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.
Quartic$variance(...)
...Unused.
clone()The objects of this class are cloneable with this method.
Quartic$clone(deep = FALSE)
deepWhether to make a deep clone.
Quantile is omitted as no closed form analytic expression could be found, decorate with FunctionImputation for numeric results.
Other kernels:
Cosine,
Epanechnikov,
LogisticKernel,
NormalKernel,
Sigmoid,
Silverman,
TriangularKernel,
Tricube,
Triweight,
UniformKernel